Question

3) Cables for a computer system to comply with quality control standards must register resistance between 0.12 and 0.14 ohms. If the actual average resistance of the cables manufactured by the company Alfa has a normal probability distribution with a mean of 0.13 ohms and a standard deviation of 0.005 ohms.

Answer the following questions:

A) What is the probability that a cable, randomly selected from a batch produced by the Alfa company, meets the specifications?

B) If four cables are needed for a specific computer model and these are taken from the batch produced by the Alfa company, find the probability that the four cables meet the specifications.

Answer 1

X : Resistance of the cables manufactured by the company Alfa

X follows a normal distribution with mean :0.13 and standard deviation : 0.005

Specifications for cables for a computer system must have resistance between 0.12 and 0.14 ohms

Probability that a cable, randomly selected from a batch produced by the Alfa company, meets the specifications

=P(0.12X 0.14)=P(X1.4)-P(X0.12)

Z-score for 0.12 = (0.12-0.13)0.005 = -2 ; Z-score for 0.14 = (0.14-0.13)/0.005 =2

From standard normal tables, P(Z-2) = 0.0228 ; P(Z2) = 0.9772

P(X1.4) = P(Z2) = 0.9772 ; P(X0.12) = P(Z-2) = 0.0228

P(0.12X 0.14)=P(X1.4)-P(X0.12)=0.9772-0.0228=0.9544

Probability that a cable, randomly selected from a batch produced by the Alfa company, meets the specifications = 0.9544

B)

Four cables are needed for a computer model and these are taken from the batch produced by the Alfa Company,

From A)

Probability that a cable, randomly selected from a batch produced by the Alfa company, meets the specifications = 0.9544

Probability that the four cables meet the specifications

= Probability that the Cable 1 meets the specifications x Probability that the Cable 2 meets the specifications x Probability that the Cable 3 meets the specifications x Probability that the Cable 4 meets the specifications

=0.9544 x 0.9544 x 0.9544 x 0.9544 = 0.829701208

Probability that the four cables meet the specifications = 0.829701208